l/v 


UNIVERSITY 


OF/    ILLINOIS 

ISSUJED-WEEKLY 


LLETIN 


Vol.  XIX  JULY  3,  1922  No.  45 

[Entered  as  second-class  matter  December  u,  1912,  at  the  post  office  at  Urbana,  Illinois,  under  the 
Act  of  August  24,  1912.  Acceptance  for  mailing  at  the  special  rate  of  postage  provided  for  in 
section  1103,  Act  of  October  3,  1917,  authorized  July  31,  1918.] 


BULLETIN  NO.  10 

BUREAU  OF  EDUCATIONAL 

COLLEGE  OF  EDUCATION 


*^ 


RELATION  OF  SIZE  OF  GLASS  TO 
SCHOOL  EFFICIENCY 

by 

BUREAU  OF  EDUCATIONAL  RESEARCH 

1     Prepared,  in  part,  from  a  report  by  P.  R.  Stevenson, 
former  Assistant,   Bureau  of  Educational  Research. 


PRICE   50  CENTS 


PUBLISHED  BY  THE  UNIVERSITY  OF  ILLINOIS,  URBANA 

1922 


BULLETIN  NO.  10 

BUREAU  OF  EDUCATIONAL  RESEARCH 
COLLEGE  OF  EDUCATION 


RELATION  OF  SIZE  OF  GLASS  TO 
SCHOOL  EFFICIENCY 

by 

BUREAU  OF  EDUCATIONAL  RESEARCH 

Prepared,  in  part,  from  a  report  by  P.  R.  Stevenson, 

former  Assistant,  Bureau  of  Educational  Research.* 


PRICE  50   CENTS 


PUBLISHED  BY  THE  UNIVERSITY  OF  ILLINOIS,  URBANA 
•    1922 


TABLE  OF  CONTENTS 


PAGE 

PREFACE 3 

I.     INTRODUCTION:    RELATION  OF  SIZE  OF  CLASS  TO  SCHOOL 

EFFICIENCY  , 5 

II.     EXISTING  CONDITIONS  IN  REGARD  TO  CLASS  SIZE 10 

III.  RELATION  OF  SIZE  OF  CLASS  IN  ELEMENTARY  SCHOOL  TO 

SCHOOL  EFFICIENCY  16 

IV.  RELATION  OF  SIZE  OF  CLASS  IN  HIGH  SCHOOL  TO  SCHOOL 

EFFICIENCY  24 

V.     SUGGESTIONS  FOR  EDUCATIONAL  EXPERIMENTATION...  37 


PREFACE 


This  investigation  was  initiated  by  Mr.  B.  R.  Buckingham, 
formerly  Director  of  the  Bureau  of  Educational  Research.  It  was 
planned  and  executed  by  him  with  the  assistance  of  Mr.  P.  R.  Steven- 
son, a  full  time  assistant  in  the  employ  of  the  Bureau  of  Educational 
Research  during  the  school  year  of  1920-21.  The  present  Director 
of  the  Bureau  of  Educational  Research  had  no  connection  with  the 
study  until  late  in  the  summer  of  1920-21.  The  portion  of  this 
report  which  deals  with  "existing  conditions  in  regard  to  class  size" 
and  "the  relation  of  size  of  class  in  high  schools  to  school  efficiency" 
is  based  upon  tabulations  made  by  employees  of  the  Bureau  of 
Educational  Research  under  Mr.  Stevenson's  direction  and  included 
by  him  in  a  report  submitted  to  the  present  Director  of  the  Bureau 
of  Educational  Research.  The  chapter  devoted  to  the  relation  of 
the  size  of  class  in  elementary  schools  to  school  efficiency  is  based 
upon  tabulations  made  from  the  original  data  under  the  immediate 
direction  of  the  present  Director.  The  concept  of  the  efficiency 
ratio  and  the  use  of  this  concept  in  the  interpretation  of  the  data 
are  entirely  the  work  of  the  present  Director  of  the  Bureau  of  Edu- 
cational Research.  The  conclusions  are  also  his  own. 

Certain  limitations  of  the  investigation,  which  the  report  dis- 
cusses in  detail,  cause  the  results  to  have  a  limited  practical  signifi- 
cance, but  it  is  thought  that  the  publication  is  jusified  for  two  rea- 
sons. In  the  first  place,  the  concept  of  school  efficiency  and  the 
analysis  of  the  conditions  which  must  be  considered  in  any  investi- 
gation relating  to  school  efficiency  should  be  helpful  to  future  inves- 
tigators not  only  of  the  question  of  class  size  but  also  of  questions 
of  other  phases  of  school  procedure.  In  the  second  place,  the  report 
emphasizes  the  need  for  careful  planning  which  will  result  in  the 
control  of  all  factors  involved  in  the  teaching  situation.  There  is 
also  emphasis  upon  the  need  for  securing  normal  conditions  if  the 
results  are  to  be  interpreted  with  reference  to  the  modification  of 
practise.  Such  analysis  and  careful  thinking  are  not  only  important 
phases  of  educational  research  but  they  are  the  foundation  upon 
which  both  the  data  collected  and  the  statistical  manipulation  of  them 
are  based. 


This  investigation  was  made  possible  through  the  cooperation 
of  Superintendent  Peter  A.  Mortenson,  of  the  Chicago  Public  Schools, 
and  of  the  school  officials  in  certain  other  Illinois  cities.  Not  only 
did  they  cooperate  by  permitting  the  collection  of  the  data,  but  they 
actually  made  substantial  contributions  to  the  project  by  furnishing 
the  test  materials.  The  teachers  in  the  schools  concerned  made  a 
substantial  contribution  by  scoring  the  tests  and  reporting  them  in 
a  convenient  form  to  the  Bureau  of  Educational  Research.  The 
writer  is  glad  to  acknowledge  the  indebtedness  of  the  Bureau  of 
Educational  Research  to  all  those  who  have  contributed  to  the 
project. 

WALTER  S.  MONROE,  Director. 
May  26,  1922. 


RELATION  OF  SIZE  OF  CLASS  TO  SCHOOL  EFFICIENCY 

CHAPTER  I 
INTRODUCTION:   ANALYSIS  OF  PROBLEM 

The  problem.  The  problem  of  this  investigation  is  to  study 
the  relation  of  the  size  of  class  to  school  efficiency,  or  what  is  the 
effect  upon  the  efficiency  of  the  school  when  the  size  of  class  is  in- 
creased or  decreased  within  certain  limits. 

Definition  of  terms:  Class.  In  the  high  school,  a  class  is  de- 
nned as  the  number  of  pupils  who  are  assigned  to  a  single  teacher 
for  instruction  during  a  single  class  period.  In  the  elementary  school, 
unless  the  instruction  has  been  departmentalized,  a  class  is  the 
number  of  pupils  assigned  to  a  room  over  which  a  teacher  has  charge. 
For  instructional  purposes,  a  teacher  in  the  elementary  school  may 
divide  a  class  into  two  or  three  groups,  but  the  total  number  of 
pupils  receiving  instruction  from  her  is  considered  a  class,  as  the 
term  is  used  in  this  study. 

School  efficiency.  Educators  have  borrowed  the  term  "effi- 
ciency" from  industry  and  business.  In  these  fields,  efficiency  is 
expressed  by  a  fraction  whose  maximum  is  1.00.  The  numerator 
of  this  fraction,  or  "efficiency  ratio/'  is  the  output,  and  the  denom- 
inator is  the  input,  or  educational  investment.  In  education,  the 
output  of  a  school  system  consists  of  the  changes  produced  in  the 
pupils,  i.  e.,  the  controls  of  conduct  that  the  school  engenders.  The 
educational  output  for  a  semester  or  a  year  is  the  total  of  all  the 
changes  that  have  been  produced  in  the  pupils  during  the  period  due 
to  the  influence  of  the  school.  The  educational  investment  includes 
many  factors,  such  as  buildings,  equipment,  textbooks,  teachers, 
supervision,  and  general  administration.  Although  it  is  not  imper- 
ative to  do  so,  it  is  probably  best  to  think  of  both  the  output  and  the 
investment  as  being  expressed  in  terms  of  the  average  for  one  pupil. 

We  are  accustomed  to  refer  to  the  educational  output  as  the 
achievements  of  the  pupils.  By  means  of  educational  tests  and 
other  instruments,  we  measure  these  achievements  in  terms  of  arbi- 
trary units.  Units  of  one  type  are  implied  in  school  marks.  Other 


units  are  defined  by  educational  tests.     In  order  to  calculate  the 
numerical  value  of  the  efficiency  ratio,  it  would  be  necessary  to  de- 
termine the  social  value  of  the  output  in  terms  of  dollars  and  cents 
or  in  terms  of  some  unit  which  might  be  made  common  to  both 
numerator  and  denominator.    Obviously,  we  are  not  prepared  to  do 
this.    However,  we  may  use  the  ratio  as  a  definition  of  school  effi- 
ciency and  inquire  into  the  probable  nature  of  the  changes  produced 
in  it  by  the  variations  of  certain  factors  upon  which  the  educational 
output  and  educational  investment  depend.     In  making  inferences 
concerning  the  fluctuations  in  the  value  of  the  efficiency  ratio,  it  is 
necessary  to  remember  that  the  production  of  certain  achievements 
may  be  of  little  value  when  viewed  in  relation  to  our  educational 
objectives.     The  attainment  of  certain  levels  of  achievement  may 
represent  an  educational  output  of  considerable  value,  but  advance- 
ment to  higher  levels  may  produce  only  slight  increases  in  the  value 
of  the  total  output  in  this  field.     For  example,  the  attainment  of 
certain  levels  of  ability  in  spelling  has  a  distinct  and  relatively  large 
social  value,  but  advancement  beyond  these  levels  is  accompanied 
by  rapidly  diminishing  increments  of  value.     Therefore,  one  must 
avoid  the  assumption  that  fluctuations  in  achievements  are  to  be 
interpreted  as  having  proportional  values  in  terms  of  social  worth. 
Factors  which  affect  school  efficiency.     For  a  given  educa- 
tional investment  per  pupil,  the  value  of  the  efficiency  ratio  is  af- 
fected when  changes  are  made  in  the  educational  output.   Methods 
of  instruction,  the  plan  of  school  organization,  or  the  procedure  of 
supervision  may  be  modified  even  when  there  is  no  change  in  the 
investment.     When  modifications  in  the  methods  of  using  the  in- 
vestment result  in  changes  in  the  educational  output,  there  are  re- 
sulting changes  in  the  value  of  the  efficiency  ratio.     On  the  other 
hand,  it  is  possible  that  material  changes  may  be  made  in  the  educa- 
tional investment  which  are    not    accompanied    by    corresponding 
changes  in  the  educational  output.     When  this  happens,  the  value 
of  the  efficiency  ratio  is  changed,  even  though  the  actual  educational 
output  has  remained  constant. 

In  many  cases,  modifications  in  the  method  of  using  the  educa- 
tional investment  are  accompanied  by  changes  in  the  magnitude  of  the 
educational  investment  as  well  as  by  changes  in  the  educational  output. 
Hence,  we  may  have  fluctuations  occurring  in  both  the  numerator 


and  the  denominator  of  the  efficiency  ratio.  It  is  possible  that  these 
fluctuations  may  be  connected  in  such  a  way  that  the  value  of  the 
efficiency  ratio  remains  constant,  or  it  may  be  that  its  magnitude 
will  vary.  Because  we  are  not  able  to  calculate  a  numerical  value 
of  the  efficiency  ratio,  a  careful  analysis  is  required  to  determine 
the  probable  changes  in  it  when  variations  occur  in  the  numerator 
and  the  denominator  simultaneously. 

The  achievements  of  pupils  are  materially  affected  by  their 
general  intelligence  or  capacity  to  learn.  Since  individual  pupils  and 
also  groups  of  pupils  have  been  shown  to  exhibit  marked  individual 
differences  when  measured  with  respect  to  this  trait,  it  is  necessary 
to  make  due  allowance  for  differences  in  general  intelligence  when 
comparing  different  school  units  with  respect  to  efficiency.  In  case 
this  is  not  done  an  error  of  interpretation  will  be  made  by  attrib- 
uting a  higher  degree  of  efficiency  to  those  units  which  consist  of 
pupils  of  superior  general  intelligence. 

The  effect  of  varying  the  size  of  class.  The  size  of  class  is 
one  item  of  the  plan  of  the  organization.  From  this  point  of  view, 
it  may  be  considered  one  of  the  methods  of  using  the  educational 
investment.  Consequently,  we  may  expect  to  find  that  changes  in 
the  size  of  class  produce  variations  in  the  achievements  of  pupils. 
The  size  of  the  class  is,  also,  one  of  the  factors  which  determines  the 
educational  investment.  In  the  elementary  school,  where  a  class 
means  the  number  of  pupils  assigned  to  a  teacher,  the  cost  of  in- 
struction per  pupil  varies  inversely  with  the  size  of  class.1  In  a  high 
school  the  size  of  class  does  not  completely  determine  the  number 
of  student  hours  of  instruction  which  a  teacher  gives,  but  it  is  a 
potent  factor  in  this  determination.  In  general,  an  increase  in  the 
size  of  class  in  the  high  school  will  tend  to  result  in  a  marked  de- 
crease in  the  educational  investment  per  pupil*  Hence,  in  studying 
the  effect  of  varying  the  size  of  class  upon  the  efficiency  of  the  school, 
it  is  necessary  for  us  to  inquire  into  the  resulting  changes  in  both 
the  educational  output  and  the  educational  investment.  It  is  only 
when  we  have  done  this  that  we  are  in  a  position  to  make  inferences 
concerning  the  effect  of  variations  in  the  size  of  class  upon  the  effi- 
ciency of  the  school. 

,*In  making  this  statement,  no  account  is  taken  of  investments  made  in  super- 
vision, in  instruction  by  special  teachers,  and  in  equipment. 


The  practical  importance  of  a  study  of  the  relation  of  class 
size  to  school  efficiency.  During  recent  years,  school  adminis- 
trators have  faced  the  problem  of  providing  instruction  for  a  rap- 
idly increasing  enrollment  and,  at  the  same  time,  of  meeting  the 
demands  from  teachers  for  increased  salaries.  In  meeting  these  two 
demands,  there  has  been  a  tendency  to  increase  the  number  of 
pupils  instructed  by  a  teacher  in  order  to  keep  the  total  educational 
expenditure  within  the  income  of  the  school  system.  In  the  elemen- 
tary school,  and  to  a  considerable  extent  in  the  high  school,  the 
number  of  pupils  instructed  by  a  teacher  has  been  increased  by 
increasing  the  size  of  classes.  It  is  obvious  that  pupils  in  large 
classes  have  less  opportunity  for  recitation  and,  in  general,  receive 
less  individual  attention  from  the  teacher,  both  within  and  outside 
of  the  class  period.  Thus,  the  question  has  naturally  been  raised 
concerning  the  effect  upon  the  efficiency  of  a  school  when  the  size 
of  the  class  is  increased.  In  the  secondary  school  added  emphasis  is 
given  to  the  question  because  certain  accrediting  agencies  require 
that  the  size  of  the  class  not  exceed  a  certain  fixed  maximum. 

Connection  between  size  of  class  and  methods  of  instruc- 
tion. It  is  necessary  to  bear  in  mind  that,  when  the  number  of 
pupils  instructed  by  a  teacher  is  increased,  there  is  a  corresponding 
increase  in  the  amount  of  work  required  of  the  teacher,  unless  there 
are  compensating  changes  in  the  methods  of  instruction.  For  ex- 
ample, according  to  our  present  methods,  it  is  customary  to  require 
a  great  deal  of  written  work  of  pupils  studying  English  composition. 
A  teacher  is  expected  to  read  with  considerable  care  the  composi- 
tions submitted  by  pupils  and  to  provide  a  systematic  procedure  for 
correcting  the  errors  made.  Thus,  an  increase  in  the  number  of 
pupils  to  be  taught  increases  the  work  required  of  the  teacher  un- 
less the  number  of  compositions  required  from  each  pupil  is  reduced 
or  a  different  system  of  handling  them  is  used.  Much  the  same 
conditions  prevail  in  a  number  of  other  subjects  in  which  notebooks 
or  other  written  work  of  some  sort  are  customarily  required.  Sim- 
ilar statements  can  be  made  with  reference  to  individual  work  with 
pupils  outside  of  the  regular  class  period.  It  is  obvious  that  there  is 
a  limit  to  the  amount  of  work  which  may  legitimately  be  required 
of  a  teacher.  When  the  optimal  teaching  load  has  been  reached, 
any  increase  in  the  number  of  pupils  assigned  to  a  teacher  should 

8 


be  expected  to  be  accompanied  by  compensating  changes  in  the  pro- 
cedure of  instruction.  When  such  changes  are  made  in  the  teaching 
procedure,  they,  as  well  as  the  size  of  the  class,  must  be  considered 
in  respect  to  the  effect  upon  the  efficiency  of  the  school. 

Limitations  of  the  present  investigation.  In  this  investiga- 
tion of  the  effect  of  varying  the  size  of  class  upon  school  efficiency, 
it  was  intended  that  all  other. factors  which  affect  either  the  achieve- 
ments of  pupils  or  the  educational  investment  should  be  kept  con- 
stant, i.  e.,  they  should  be  the  same  for  classes  of  different  sizes. 
No  information  is  available  to  show  the  extent  to  which  this  inten- 
tion was  realized  except  in  the  case  of  the  quality  of  the  pupil  ma- 
terial. Group  intelligence  tests  were  used  to  secure  equivalence  of 
capacity  to  learn  in  the  two  groups  of  pupils.  The  possibility  of  a 
lack  of  equivalence  of  such  factors  as  home  environment,  nation- 
ality, attitude  toward  school  work,  previous  school  experience  with 
respect  to  size  of  class,  time  of  day  (applies  only  to  high  school), 
etc.,  makes  it  necessary  to  exercise  due  caution  in  interpreting  the 
results  of  the  investigation. 

So  far  as  the  present  writer  is  aware,  the  instruction  that  pre- 
vailed in  the  groups  concerned  in  this  investigation  involved  no  un- 
usual features,  and  the  same  methods  of  instruction  were  followed 
in  the  two  types  of  classes.  It  is  possible  that  the  highest  degree 
of  efficiency  for  classes  of  a  given  size  would  be  attained  if  the 
methods  of  instruction  were  selected  with  particular  reference  to 
this  size  of  class.  It  would  not  be  surprising  to  find  that  methods 
of  instruction  which  were  most  effective  in  small  classes  would  be 
considerably  less  effective  with  large  classes,  and  that  methods  well 
suited  to  the  handling  of  large  classes  would  not  give  the  best  results 
when  used  with  small  classes.  This  possibility  was  not  considered 
in  this  investigation.  Hence,  the  findings  should  not  be  accepted  as 
final.  There  is  still  need  for  an  investigation  in  which  methods 
of  instruction  are  adapted  to  size  of  class. 

Finally,  it  must  be  remembered  that  the  problem  of  the  size  of 
class  is  not  entirely  a  problem  of  the  efficiency  of  the  school.  It  is 
also  a  problem  of  the  teacher.  It  is  not  humane  and  it  is  not  socially 
profitable  to  assign  teaching  loads  so  heavy  that  teachers  become 
overworked.  The  problem  of  the  teacher  was  not  considered  in  this 
investigation. 


CHAPTER  II 
EXISTING  CONDITIONS  IN  REGARD  TO  CLASS  SIZE 

In  order  that  the  significance  of  the  two  investigations  to  be 
reported  in  the  following  chapters  may  be  more  fully  appreciated, 
certain  facts  are  presented,  concerning  the  size  of  class  under  present 
school  conditions  in  Illinois. 

Size  of  class  in  elementary  schools  in  Illinois  outside  of 
Chicago.  Data  with  reference  to  the  size  of  class  in  the  elementary 
schools  of  the  state,  outside  of  Chicago,  were  secured  by  sending  a 
questionnaire  to  the  superintendent  of  public  schools  in  all  cities  and 
towns  listed  in  the  Illinois  School  Directory  for  1920-21  as  having 
six  or  more  elementary  teachers.  The  questionnaire  asked  for  the 
number  of  elementary  teachers  having  classes  of  the  following  sizes : 
less  than  20,  20  to  29,  30  to  39,  40  to  49,  and  50  and  over.  This 
information  was  requested  for  each  of  the  school  years  of  1918-19, 
1919-20,  and  1920-21.  Complete  reports  were  received  from  180 
cities  and  towns.  These  are  summarized  in  Table  I.  The  total 
number  of  classes  for  which  a  report  was  secured  varied  from  9,422, 
1918-19,  to  10,403,  in  1920-21.  The  median  size  of  class  varied  from 
41.4  pupils,  1918-19,  to  43.3  pupils,  in  1919-20.  In  1920-21,  the  size 
of  class  was  slightly  less  than  that  for  the  preceding  year.  This 
table  also  shows  that,  in  the  cities  reporting,  slightly  more  than  3 
percent  of  all  classes  contained  50  or  more  pupils.  On  the  other 
hand,  between  7  and  8  percent  of  the  classes  had  less  than  30  pupils. 
The  greatest  change  in  regard  to  the  size  of  class  during  this  period 
was  in  the  marked  decrease  in  the  number  of  classes  having  between 
30  and  39  pupils.  During  the  school  year,  1918-19,  the  size  of  slight- 
ly more  than  one-third  of  the  classes  fell  within  these  limits.  During 
the  other  two  school  years,  covered  by  this  study,  less  than  one- 
fifth  of  the  classes  came  within  these  limits  of  size.  This  change  is 
offset  by  a  corresponding  increase  in  the  number  of  classes  having 
between  40  and  49  pupils.  Although  the  span  of  years  covered  by 
this  table  is  insufficient  to  justify  conclusions  with  reference  to  the 
trend  of  the  size  of  class,  Table  I  suggests  that  there  is  a  tendency,  in 

10 


TABLE  I.       SIZE   OF   CLASSES   IN   THE  ELEMENTARY  SCHOOLS   OF    180 
ILLINOIS   CITIES   FOR    1918-21. 


Number  in 
Classes 

1918-19 

1919-20 

1920-21 

Number 
of  Classes 

Percent 
of  Classes 

Number 
of  Classes 

Percent 
of  Classes 

Number 
of  Classes 

Percent 
of  Classes 

50 

313 
5134 
3264 
598 
113 

3.3 
54.5 
34.6 
6.3 
1.3 

342 
6865 
1845 
646 
110 

3.5 
70.0 
18.8 
6.6 
1.1 

350 
7161 
2050 
719 
123 

3.4 
68.8 
19.7 
6.9 
1.2 

40-49  

30-39 

20-29  

Less  than  20 

Total.  . 

9422 

100.0 

9808 

100.0 

10403 

100.00 

Median. 

41.4 

43.4 

43.2 

the  elementary  schools  of  Illinois  outside  of  Chicago,  to  assign  from 
40  to  50  pupils  to  a  teacher. 

Size  of  class  in  Chicago  public  schools,   October,   1920. 

Because  the  two  investigations  to  be  reported  later  were  carried  on, 
for  the  most  part,  in  certain  schools  in  Chicago,  it  was  thought  de- 
sirable to  compile  separately  the  facts  relating  to  class  size  in  Chi- 
cago. The  information  was  taken  from  the  records  of  the  superin- 
tendent of  schools.  One-half  of  the  elementary  schools  were  selected 
at  random,  but  all  of  the  high  schools  were  included.  Information, 
with  reference  to  the  size  of  class  in  each  grade,  is  summarized  in 
Table  II.  Below  the  ninth  grade,  the  classes  are  noticeably  larger 
than  in  the  high  school.  The  median  size  of  class  is  approximately 
46  pupils.  In  the  high  school,  a  greater  degree  of  variability  is 
shown  in  the  size  of  class.  Approximately  14  per  cent  of  the  classes 
have  fewer  than  20  pupils.  The  median  size  of  class  for  the  high 
school  is  slightly  over  30  pupils.  It  will  be  noted  that  the  classes  for 
the  first  year  are  larger  than  those  for  the  following  years.  Of  the 
183  classes,  178  reported  as  having  from  50  to  54  pupils,  are  classes 
in  physical  training.  A  number  of  these  have  more  than  54  pupils. 
The  size  of  high  school  classes  is  given  by  subjects  in  Table  III. 
The  median  size  of  class  for  the  different  subjects  ranges  from  20.0, 


11 


TABLE  II.       SIZE  OF  CLASSES  IN  CHICAGO   SCHOOLS,  OCTOBER,    1920. 


Grades 

Less 
than 

Number  in  class 

55 

and 

To- 
tal 

Med- 
ian 

10 

10-14 

15-19 

20-24 

25-29 

30-34 

35-39 

40-44 

45-49 

50-54 

over 

1 

3 

1 

6 

20 

40 

120 

248 

87 

36 

561 

46.8 

2 

1 

2 

1 

6 

11 

102 

247 

38 

1 

409 

46.7 

3 

1 

1 

1 

3 

18 

96 

211 

48 

q 
*j 

382 

46.7 

4 

1 

2 

3 

15 

90 

207 

39 

257 

46.6 

5 

1 

2 

4 

79 

215 

48 

i 

350 

47.1 

6 

3 

3 

1 

2 

12 

103 

183 

27 

4 

338 

46.2 

7 

2 

2 

15 

92 

180 

32 

2 

326 

46.4 

8 

1 

4 

54 

79 

117 

15 

48 

318 

44.8 

i 

Total 

• 

Elementary 

9 

9 

13 

42 

169 

761 

1618 

334 

96 

3041 

46.6 

Schools 

9 

36 

108 

224 

556 

613 

850 

683 

254 

98 

92 

3474 

32.3 

10 

24 

84 

202 

342 

378 

401 

283 

136 

17 

69 

1936 

29.3 

11 

14 

60 

90 

178 

148 

189 

119 

31 

10 

19 

858 

27.8 

12 

15 

27 

64 

67 

81 

93 

77 

29 

2 

3 

458 

28.4 

Total 

H.S. 

89 

279 

580 

1143 

1220 

1533 

1162 

450 

87 

183 

6726 

30.2 

for  German,  up  to  34.5,  for  arithmetic.  If  physical  education  is  in- 
cluded, the  maximum  median  class  is  43.8.  However,  the  most  sig- 
nificant aspect  of  the  table  is  the  wide  variation  in  the  size  of  class 
for  a  given  subject.  With  few  exceptions,  there  are,  in  each  subject, 
classes  having  10  or  less  pupils  and  also  classes  having  more  than 
45  pupils.  The  exceptions  are  shop  work,  in  which  the  number  of 
pupils  is  probably  limited  by  the  equipment,  office  practise,  of  which 
there  are  only  37  classes  in  the  entire  school  system,  chemistry,  home 
economics,  botany,  zoology  and  agriculture,  in  which  equipment 
again  probably  limits  the  size  of  class.  In  German  there  are  no 
classes  having  more  than  34  pupils,  but  there  are  only  8  classes  in 
the  entire  system. 

Opinions  of  city  superintendents  in  regard  to  the  best  size 
of  class.  A  questionnaire  was  sent  to  the  city  superintendents  of 
public  schools  in  all  cities  in  the  United  States  having  a  population 


12 


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TABLE  IV.       IDEAL  SIZE  OF  CLASSES  AS  INDICATED  BY  270  SUPERINTEND- 
ENTS IN  CITIES  OF  25,000  OR  MORE  POPULATION. 


Grades 

Score 

1,  2,  3, 

4,  5,  6, 

7,  8,  9, 

10,  11,  12 

55-59 

1 

50-54 

1 

1 

45-49 

2 

2 

1 

40-44 

16 

18 

15 

2 

35-39 

53 

73 

35 

4 

30-34 

95 

95 

104 

33 

25-29 

52 

42 

58 

95 

20-24 

20 

21 

48 

95 

0-19 

30 

18 

9 

16 

Total  

269 

270 

270 

246 

Median.  .  .  . 

31.7 

32.8 

31.0 

25.6 

of  25,000  or  more,  as  shown  by  the  directory  issued  by  the  Bureau 
of  Education.  The  questionnaire  asked  the  superintendents  to  indi- 
cate the  ideal  size  of  class  in  their  opinion  for  grades  one  to  three, 
four  to  six,  seven  to  nine,  and  ten  to  twelve.  Replies  from  270  cities 
are  summarized  in  Table  IV.  One  of  the  most  interesting  things 
about  this  table  is  the  wide  range  of  opinion  which  it  indicates.  A 
considerable  number  of  superintendents  would  have  fewer  than  20 
pupils  in  each  class.  Other  superintendents  appear  to  consider  classes 
of  40  or  more  ideal.  One  superintendent  indicates  that  he  would 
be  satisfied  with  classes  of  55  pupils  in  the  primary  grades.  The 
ideal  median  size  of  class  below  the  high  school  ranges  from  31.0, 
for  the  junior  high  school,  to  32.8,  for  the  intermediate  grades.  In 
the  senior  high  school,  the  ideal  median  of  class  is  25.6  pupils. 

The  problem  of  class  size.  Although  Table  IV  is  based  upon 
replies  from  superintendents  distributed  over  the  United  States,  and 
the  preceding  tables  refer  to  existing  conditions  in  Illinois,  we  are 
probably  justified  in  pointing  out  that  a  marked  difference  exists 
between  theory  and  practise.  The  prevailing  practise  in  the  elemen- 
tary schools  of  the  state  outside  of  Chicago  centers  around  classes 


14 


having  from  40  to  45  pupils.  The  median  ideal  size  of  class  is  only 
slightly  above  30.  Thus,  it  appears  that  the  practical  problem  in 
which  school  superintendents  are  interested  relates  to  a  determina- 
tion of  the  relative  efficiency  of  classes  enrolling  from  25  to  35  pupils 
as  compared  with  classes  enrolling  from  40  to  45  pupils. 

For  the  high  school,  we  have  no  data  relating  to  the  size  of 
class  in  Illinois  except  for  the  city  of  Chicago.  The  median  ideal  size 
is  approximately  25.  The  median  actual  size  is  approximately  30. 
It,  therefore,  appears  that  the  practical  problem  in  the  high  school 
relates  to  the  relative  efficiency  of  classes  enrolling  from  20  to  30 
pupils  as  compared  to  those  enrolling  from  25  to  35. 


15 


CHAPTER  in 

RELATION  OF  SIZE  OF  CLASS  IN  ELEMENTARY  SCHOOL 
TO  SCHOOL  EFFICIENCY 

General  plan  of  the  study  in  the  elementary  school.     In 

order  to  study  the  effect  of  variations  in  the  size  of  class  upon  the 
achievements  of  pupils,  it  is  necessary  to  hold  constant  or  to  measure 
the  other  factors  which  affect  their  achievements.  It  was  planned 
to  keep  the  teacher  constant  by  having  both  a  large  class  and  a  small 
class  taught  by  the  same  teacher.  Since  the  plan  of  organization  in 
the  elementary  school  makes  it  impossible  for  the  same  teacher  to 
instruct  two  classes  at  the  same  time,  it  was  necessary  to  have  a  teach- 
er instruct  the  two  types  of  classes  during  two  consecutive  semesters. 
It  was  arranged  to  have  some  of  the  teachers  instruct  a  large  class 
during  the  first  semester  and  a  small  class  during  the  second  semes- 
ter. Other  teachers  instructed  a  small  class  during  the  first  semester 
and  a  large  class  during  the  second  semester.1 

In  order  to  keep  the  pupil  material  as  nearly  constant  as  pos- 
sible, "one  hundred  percent  promotion"  was  secured  at  the  end  of 
the  first  semester  in  albof  the  experimental  groups.  When  a  teacher 
instructed  a  large  class  during  the  first  semester  a  number  of  pupils 
were  sent  to  another  teacher  at  the  beginning  of  the  second  semester. 
The  pupils  remaining  formed  a  small  class.  In  doing  this,  an  effort 
was  made  to  select  pupils  so  that  those  remaining  would  form  a 
small  class  having  approximately  the  same  average  mental  age  and 
the  same  variability  of  this  trait.  When  a  teacher  instructed  a  small 
class  during  the  first  semester,  pupils  were  added  at  the  beginning 
of  the  second  semester,  but  care  was  exercised  to  have  these  pupils 
such  that  the  average  mental  age  of  the  class  would  not  be  materially 
affected. 

This  investigation,  which  began  in  October,  1920,  was  confined 
to  classes  in  grades  II,  V,  and  VII.  Some  of  the  experimental  groups 
were  organized  in  the  B  sections  of  these  grades  and  the  others  in 
the  A  sections-  At  the  beginning  of  the  second  semester  the  B  sec- 

lrThis  investigation  was  carried  on  in  five  elementary  schools  in  Chicago:  Wash- 
ington, Cleveland,  Lowell,  Farragut,  and  Hibbard. 

16 


tions  became  A  sections  of  the  same  grade  and  the  A  sections  be- 
came B  sections  of  the  next  higher  grade.  We  shall,  however,  refer 
to  the  grades  simply  as  II,  V,  and  VII.  Data  for  only  those  pupils 
who  attended  both  the  large  class  and  the  small  class  and  who  took 
all  of  the  tests  given  are  included  in  the  following  tabulations. 

The  size  of  the  experimental  classes.  In  the  second  grade 
there  were  eleven  experimental  classes,  three  small  the  first 
semester  and  large  the  second,  and  eight  of  the  opposite  type.  If 
one  class,  enrolling  only  18  pupils  when  considered  a  large  class,  is 
excluded,  the  small  classes  range  from  33  to  44  and  the  large  from 
45  to  54.  The  differences  in  the  size  of  the  paired  groups  range  from 
4  to  13,  the  average  being  approximately  eleven  pupils.  In  the  fifth 
grade  there  were  thirteen  experimental  classes,  three  small  the  first 
semester  and  large  the  second,  and  ten  of  the  opposite  type.  The 
small  classes  range  in  size  from  33  to  45  and  the  large  from  42  to 
52.  The  differences  in  the  size  of  the  paired  groups  range  from  4 
to  14,  the  average  difference  being  approximately  9.  In  the  seventh 
grade  there  were  only  five  experimental  classes,  three  of  one  type 
and  two  of  the  other.  The  small  classes  ranged  from  35  to  44  and 
the  large  from  42  to  49.  The  average  difference  in  size  was  approx- 
imately 7.  It  should  be  noted  that  in  both  the  fifth  and  seventh 
grades  there  is  some  overlapping  in  the  size  of  the  two  types  of 
classes.  Some  "large  classes"  are  smaller  than  certain  "small  classes." 

Data  collected.  In  the  second  grade,  the  Dearborn  Group  In- 
telligence Test  and  Pressey  Primer  Scale  were  given  at  the  begin- 
ning of  the  experiment.  In  this  grade,  achievement  was  measured 
by  giving  the  Indiana  Scale  of  Attainment,  No.  1.  Form  1  was  given 
in  October,  Form  2  in  January,  and  Form  1  was  used  again  at  the 
end  of  the  year.  In  grades  V  and  VII,  the  Illinois  General  Intelli- 
gence Scale  was  used.  The  achievements  of  the  pupils  were  meas- 
ured in  arithmetic,  silent  reading,  language,  and  spelling.  In  arith- 
metic and  reading,  the  measurements  were  secured  by  means  of  the 
tests  included  in  the  Illinois  Examination.  Form  1  was  used  for  the 
first  and  third  testings  and  Form  2  for  the  second.  In  language, 
Charters'  Diagnostic  Language  Test  for  pronouns  was  used.  Form 
1  was  given  in  October  and  in  May.  Form  2  was  used  for  the  Jan- 
uary testing.  In  spelling,  20  words  were  selected  from  columns  N 
and  R  of  the  Buckingham  Extension  of  the  Ayres'  Spelling  Scale. 

17 


For  the  first  and  third  testings,  the  words  were  selected  by  beginning 
at  the  bottom  of  these  columns  and  choosing  alternate  words.  The 
words  for  the  second  testing  were  taken  from  these  columns,  begin- 
ning with  the  next  to  the  last  word  and  taking  alternate  ones. 

Administration  of  tests  and  collection  of  data.  All  the  tests 
were  administered  and  scored  by  the  teacher.  As  a  preparation  for 
this  work,  the  teachers  were  called  together  and  given  definite  in- 
structions concerning  the  nature  of  the  tests  and  the  plan  of  admin- 
istration. In  this  connection,  the  tests  were  administered  to  the 
teachers  in  order  to  illustrate  to  them  the  procedure  to  be  used  with 
the  pupils.  All  of  the  tests  are  highly  objective  with  reference  to  the 
scoring,  and  samplings  of  the  test  papers  failed  to  reveal  any  large 
errors  in  this  work.  The  teachers  reported  the  data  for  each  pupil 
on  an  individual  record  card.  This  card  contained  spaces  for  each 
score  and  each  test  as  well  as  for  data  with  reference  to  the  size  of 
class  in  which  the  pupil  was  taught  during  each  semester.  The 
dates  of  testing  were  approximately  as  follow:  October  20th,  Feb- 
ruary 20th,  and  May  20th. 

Method  of  summarizing  the  data.  The  data  summarized 
were  limited  to  the  scores  of  only  those  pupils  who  were  members 
of  both  a  large  class  and  a  small  class,  and  who  were  present  at  all 
three  testing  periods.  The  scores  of  all  pupils  in  a  grade  (including 
both  A  and  B  sections),  who  had  been  taught  in  the  same  type  of 
class,  were  assembled  for  each  of  the  three  testings.  For  example, 
the  October  arithmetic  scores  for  all  fifth  grade  pupils  who  were 
taught  in  large  classes  during  the  first  semester  and  in  small  classes 
during  the  second  semester  were  assembled  in  one  distribution.  An- 
other distribution  was  made  for  the  January  scores  and  a  third  one 
for  the  May  scores.  Three  corresponding  distributions  were  made 
for  the  arithmetic  scores  of  the  pupils  who  were  taught  in  small 
classes  during  the  first  semester  and  in  large  classes  during  the  sec- 
ond. Thus,  there  were  obtained  six  distributions  for  each  achieve- 
ment score.  One  measure  of  tne  gain  in  achievement  made  by  a 
group  of  pupils  during  the  first  semester  was  found  by  subtracting 
the  average  of  the  October  scores  from  the  average  of  the  January 
scores.  Another  measure  of  the  gain  was  found  by  subtracting  the 
median  October  score  from  the  median  January  score.  In  a  similar 
manner,  the  gains  for  the  second  semester  were  obtained  by  sub- 

18 


tracting  the  average  and  the  median  January  scores  from  the  cor- 
responding May  scores. 

la  calculating  these  gains,  no  account  was  taken  of  the  possible 
non-equivalence  of  the  different  forms  of  the  tests  used.  In  fact, 
no  accurate  information  concerning  the  equivalence  of  the  duplicate 
forms  is  available,  except  for  the  tests  in  reading  and  arithmetic. 
The  duplicate  forms  of  these  two  tests  have  been  shown  to  be  ap- 
proximately equal.2  Since  Form  1  was  used  twice,  and  the  average 
and  the  median  scores  calculated  from  it  were  used  both  as  subtra- 
hends and  minuends,  any  non-equivalence  of  the  forms  will  not  af- 
fect the  comparisons  of  gains  made  in  the  following  table. 

The  scores  of  the  different  tests  are  expressed  in  terms  of  dif- 
ferent units.  Thus,  before  any  combination  of  the  results  from  the 
different  tests  can  be  made,  it  is  necessary  to  express  the  gains  in 
terms  of  a  common  unit.  The  usual  assumption  in  such  cases  is  that 
the  standard  deviation  of  the  distribution  of  scores  represents  the 
same  increment  of  ability  for  one  test  and  in  one  grade  as  in  another. 
On  the  basis  of  this  assumption,  the  stardard  deviation  was  calcu- 
lated for  six  of  the  different  distributions  of  scores  for  each  test  in 
a  given  grade,  and  the  average  of  these  six  standard  deviations  was 
used  as  a  divisor  to  reduce  the  gains  to  a  basis  of  a  common  unit. 
For  example,  during  the  first  semester  the  fifth  grade  pupils  taught 
in  large  classes  in  arithmetic  made  a  gain  of  12.0  points.3  During 
the  second  semester  they  made  a  gain  of  7.2  points.  The  gains  for 
the  pupils  taught  in  small  classes  in  arithmetic  were  6.5  and  5.65. 
The  average  standard  deviation  of  the  six  distributions  of  arithmetic 
scores  is  17.441.  Dividing  these  gains  by  this  average  standard  de- 
viation, we  secure  as  quotients  the  entries  (.68,  .41,  .36,  and  .32)  to 
be  found  in  Table  V. 

In  calculating  the  average  gains  for  the  two  types  of  classes, 
the  simple  average  of  the  two  gains  has  been  used  rather  than  the 
weighted  average,  although  the  two  groups  are  not  even  approxi- 
mately equivalent  in  size.  Since  oi^r  purpose  in  taking  this  average 
is  to  eliminate  any  differences  in  the  course  of  study  or  in  the  edu- 

2Monroe,  Walter  S.     "The  Illinois  Examination."     University  of  Illinois  Bulle- 
in,  Vol.  19,  No.  9,  Bureau  of  Educational  Research  Bulletin,  No.  6.    Urbana:  Uni- 
sity  of  Illinois,  1921. 
"These  gains  were  calculated  from  the  average  of  the  scores. 

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cational  opportunities  offered  in  the  two  semesters  and  also  any 
practise  effect  due  to  acquaintance  with  the  tests,  it  seemed  unwise 
to  weight  the  averages  on  the  basis  of  the  number  of  pupils  in  the 
two  groups.  To  have  used  the  weighted  averages  in  this  case  would 
have  resulted  in  ^grVing  greater  weight  to  the  gains  made  by  one 
group  of  pupils  simply  because  this  group  happened  to  be  larger. 

Achievements  of  the  two  groups  approximately  equal. 
Table  V4  summarizes  the  data  with  reference  to  the  gains  made  by 
the  two  groups.  The  column  headed  "Number  of  pupils"  gives  the 
number  of  pupils  whose  records  were  used  in  the  tabulations.  (A 
pupil's  record  was  discarded  if  he  was  not  a  member  of  both  the 
small  class  and  the  large  class  and  if  he  did  not  take  all  tests.)  The 
average  size  of  class  is  computed  from  the  total  enrollment.  The 
computation  of  the  gains  has  just  been  explained.  In  interpreting 
the  table,  attention  should  be  focused  upon  the  differences.  A  posi- 
tive difference  means  that  the  large  class  is  superior  in  achievement, 
and  a  negative  difference  that  the  small  class  is  superior.  At  the 
bottom  of  each  difference  column  the  differences,  calculated  from 
the  averages  and  also  from  the  medians,  are  summarized.  This 
summary  is  a  total  and  not  an  average.  To  find  the  average  it  is 
necessary  to  divide  by  3.  All  of  the  totals  of  the  differences  fall 
between  +1.00  and  — 1.00.  Six  of  the  10  differences  are  negative, 
and  only  in  the  case  of  reading  rate  are  the  difference  between  the 
averages  and  the  difference  between  the  medians  both  positive.  In 
the  last  three  columns  of  the  table,  We  have  the  totals  and  not  aver- 
ages. To  find  the  average,  it  would  be  necessary  to  divide  by  4  in 
the  second  grade  and  by  5  in  each  of  the  other  two  grades.  Here, 
again,  the  negative  differences  predominate,  although  none  of  them 
are  very  large.  The  last  two  entries  in  the  last  column  are  essentially 
grand  totals  and  may  be  considered  to  summarize  the  entire  table. 
To  find  the  average  difference,  each  of  these  numbers  should  be  di- 
vided by  14.  The  quotients  obtained  would  be  — .04  and  — .06. 
Thus,  in  general,  this  table  indicates  that  there  is  little  if  any  superi- 
ority in  the  achievements  of  pupils  in  the  small  classes  over  those 
of  pupils  in  the  larger  classes. 


'The  entries  in  the  column  headed  "Reading  Rate"  in  the  second  grade  arc 
based  upon  the  Pressey  Word  Recognition  Test. 

21 


An  examination  of  Table  V  reveals  the  fact  that,  in  general,  the 
gains  between  the  first  and  second  testings  are  much  larger  than 
those  between  the  second  and  third  testings.  This  condition  em- 
phasizes the  necessity  for  equalizing  the  effect  of  acquaintance  with 
the  test  and  practise  effect.  If  all  of  the  experimental  groups  had 
been  taught  as  large  classes  the  first  semester  and  small  classes  the 
second,  the  gains  for  the  large  classes  would  greatly  exceed  the  gains 
for  the  small  classes;  but  this  would  be  due  primarily  to  the  effect 
of  acquaintance  with  the  test  and  the  practise  effect. 

When  Table  V  is  examined  with  reference  to  the  conditions  in 
the  different  grades  we  find  that  the  gains  are  relatively  greater  for 
the  small  classes  in  the  fifth  grade  than  in  either  the  second  or  the 
seventh  grade.  However,  the  number  of  pupils  is  so  small  for  the 
two  groups  in  the  seventh  grade  and  the  groups  differ  so  little  in  size 
that  only  slight  significance  can  be  attached  to  the  results.  Even  in 
the  second  and  fifth  grades  it  is  unfortunate  that  the  experimental 
groups  are  not  more  nearly  equal  in  size.  It  is  possible  that  if  the 
experiment  had  included  a  larger  number  of  classes  which  were  small 
the  first  semester  and  large  the  second  different  results  might  have 
been  obtained. 

When  the  gains  for  the  different  subjects  are  examined  we  find 
that  in  language  the  gains  for  the  small  classes  are  consistently 
greater  than  the  gains  for  the  large  classes.  This  is  not  true  for  any 
other  subject.  Although  in  spelling  the  total  of  the  gains  is  distinctly 
negative,  in  both  arithmetic  and  reading  comprehension  the  total 
when  computed  by  one  method  is  negative  and  in  the  other  case  is 
approximately  0.  Reading  rate  in  the  seventh  grade  is  the  only  case 
in  which  the  large  class  is  distinctly  superior  in  achievement. 

Conclusion:  the  relation  of  the  size  of  class  to  school  effi- 
ciency. Since  Table  V  indicates  that,  on  the  whole,  there  is  little 
difference  between  the  achievements  of  the  pupils  when  taught  in 
large  classes  and  their  achievements  when  taught  in  small  classes, 
one  might  infer  that  the  efficiency  of  a  school  would  be  materially 
increased  by  the  formation  of  large  classes,  because  the  educational 
output  would  be  approximately  the  same  and  the  educational  invest- 
ment would  be  materially  decreased.  However,  it  is  doubtful  that 
the  present  investigation  justifies  such  a  conclusion.  In  the  first 
place,  it  is  obvious  that  only  certain  achievements  of  pupils  have 

22 


been  measured.  Even  in  the  fields  of  the  four  subjects  in  which  tests 
were  given  we  are  not  justified  in  claiming  that  all  achievements  of 
the  pupils  were  measured.  The  arithmetic  tests  used  were  confined 
to  the  operations  and  to  only  certain  types  of  examples  within  this 
division  of  arithmetic.  In  silent  reading,  the  test  used  is  very  limited 
in  scope.  Similarly,  the  tests  in  language  and  spelling  possess  very 
definite  limitations  with  respect  to  scope.  There  is  some  justification 
for  assuming  that  the  measurements  made  may  be  considered  in- 
dices of  the  total  achievements  of  the  pupils  not  only  in  the  fields 
of  the  four  subjects  in  which  the  tests  were  given  but  also  in  the 
field  of  instruction  in  the  grades  concerned.  However,  the  thesis 
that  the  measures  of  achievement  secured  in  this  investigation  are 
indices  of  the  total  achievement  is  largely  an  assumption,  and  in  in- 
terpreting the  results  it  is  necessary  to  recognize  this  fact.  It  is 
possible  that,  if  other  tests  had  been  used  or  if  the  achievements  of 
the  pupils  had  been  more  completely  measured  by  including  tests 
in  other  subjects,  the  results  might  have  been  different. 

In  the  second  place,  it  must  be  remembered  that  the  size  of  the 
"small  classes"  was  not  less  than  33  (with  one  exception),  and  in  a 
few  cases  the  enrollment  was  as  much  as  44  or  45.  The  large  classes 
ranged  in  size  from  42  to  54.  The  average  difference  between  the 
pairs  of  experimental  groups  ranged  from  7  in  the  seventh  grade  to 
11  in  the  second  grade.  These  conditions  with  reference  to  the  size 
of  the  experimental  groups  constitute  a  very  significant  limitation  of 
the  investigation.  One  is  not  warranted  in  making  inferences  from 
the  facts  of  Table  V  with  reference  to  the  relative  efficiency  of  classes 
of  20  to  25  pupils  as  compared  with  classes  of  35  to  45  pupils.  No 
application  should  be  made  except  within  the  limits  of  size  defined 
by  the  experimental  groups. 


23 


CHAPTER  IV 

RELATION  OF  SIZE  OF  CLASS  IN  HIGH  SCHOOL 
TO  SCHOOL  EFFICIENCY 

General  plan  of  the  study  in  the  high  school.  In  the  inves- 
tigation in  the  high  school  it  was  arranged  to  have  both  a  large  class 
and  a  small  class  in  a  given  subject  instructed  by  the  same  teacher 
during  the  same  semester.  This  made  it  necessary  to  restrict  the 
experiment  to  teachers  who  were  instructing  two  or  more  sections 
of  the  same  subject.  When  a  teacher  was  instructing  two  sections, 
pupils  were  shifted  on  the  basis  of  their  intelligence  scores  so  that 
the  average  quality  of  pupil  material  was  approximately  the  same 
in  the  two  sections.  Thus,  both  classes  would  include  some  bright, 
some  medium,  and  some  dull  pupils.  When  a  teacher  had  four 
sections  of  the  same  subject,  the  pupils  were  shifted  so  that  a  large 
class  and  a  small  class  would  be  obtained,  consisting  of  relatively 
bright  pupils.  The  less  capable  pupils  were  also  divided  into  two 
classes,  one  large  and  one  small. 

In  establishing  the  two  types  of  class,  there  was  considerable 
variation  in  the  size  of  both  the  large  classes  and  the  small  classes. 
The  small  classes  varied  in  size  from  12  to  26  pupils.  The  large 
classes  varied  in  size  from  23  to  45  pupils.  The  average  size  of  the 
large  classes  was  36.5  and  that  of  the  small  classes,  20.8.  The  dif- 
ferences in  the  size  of  the  paired  classes  ranged  from  6  to  26. 

Source  of  data.  This  study  was  carried  on  in  four  large  high 
schools  in  Chicago  and  in  the  high  schools  of  three  other  Illinois 
cities.1  During  the  first  semester  of  1920-21,  the  experiment  was 
carried  on  in  beginning  tenth  grade  classes.  During  the  second 
semester  of  that  year  the  study  was  confined  to  classes  completing 
the  first  year  of  high  school  work.  In  the  following  tables  no  dis- 
tinction is  made  between  classes  for  the  two  grades.  Records  were 
secured  for  67  pairs  of  classes,  enrolling  3,821  pupils.  The  project 

lrThe  high  schools  in  Chicago  were  Lane  Technical,  Tilden  Technical,  Harrison 
Technical,  and  Hyde  Park.  The  three  other  Illinois  cities  were  Macomb,  Shelby- 
ville,  and  West  Aurora. 

24 


was  begun  by  giving  the  Terman  Group  Test  of  Mental  Ability  to 
all  pupils  concerned,  about  October  15,  1920.  Some  pupils  in  the 
high  schools  outside  of  Chicago  were  given  the  Illinois  General  In- 
telligence Scale  or  the  Chicago  Group  Intelligence  Test.  As  soon 
as  the  results  of  the  testing  could  be  assembled,  the  large  classes 
and  small  classes  were  arbitrarily  formed,  following  the  method  in- 
dicated above. 

The  educational  output,  or  the  achievements  of  the  pupils,  was 
measured  by  requiring  each  teacher  to  give  the  same  final  examina- 
tion to  both  types  of  classes.  A  check  upon  this  measurement  of 
achievement  was  secured  by  using  the  "term  grades"  of  the  pupils. 
It  is  generally  recognized  that  "term  grades,"  as  well  as  examina- 
tions set  by  teachers,  are  highly  subjective.  However,  in  this  case 
the  same  teacher  administered  the  same  examination  to  both  the 
small  class  and  the  large  class.  The  same  teacher  also  gave  the 
"term  grades."  Thus,  there  is  in  no  place  a  comparison  between 
either  "term  grades"  or  "examination  grades"  given  by  different 
teachers.  This  tends  to  eliminate  the  subjective  factor  of  these 
measures.  In  addition,  it  may  be  noted  that  we  are  concerned  with 
the  average  "grades"  of  relatively  large  groups  of  pupils  and  not 
with  the  "grades"  of  individual  pupils. 

A  limitation.  The  plan  of  carrying  on  the  experiment  implies 
the  assumption  that  the  achievements  of  the  pupils  in  the  large 
classes  were  equal  to  the  achievements  of  the  pupils  in  the  small 
classes  at  the  beginning  of  the  experimental  period.  There  was  no 
attempt  to  measure  the  achievements  of  pupils  in  the  subjects  con- 
cerned at  the  beginning  of  the  experiment.  In  the  first  semester,  the 
two  types  of  classes  were  not  organized  until  after  the  high  schools 
had  been  in  session  several  weeks.  In  the  case  of  the  classes  used 
during  the  second  semester,  the  pupils  had  received  an  entire  semes- 
ter of  instruction  in  regular  classes.  It  is  true  that  the  sections 
were  formed  so  that  the  average  general  intelligence  of  the  paired 
classes  was  approximately  equal,  but  this  probably  does  not  justify 
the  assumption  of  equivalent  achievements. 

Details  of  administration.  The  intelligence  tests  were  admin- 
istered and  scored  by  the  teachers.  As  preparation  for  this  work, 
the  teachers  were  called  together  and  given  definite  instructions  con- 
cerning the  nature  of  the  tests.  The  tests  were  also  administered 


C, 


25 


to  them.  They  were  then  required  to  score  their  own  papers.  All 
the  tests  used  were  highly  objective  with  reference  to  scoring,  and 
a  sampling  of  the  test  papers  of  the  pupils  failed  to  reveal  any  large 
errors  in  this  work.  Since,  in  the  use  of  the  intelligence  test  scores, 
comparisons  are  always  made  between  the  pupils  or  groups  of  pupils 
under  the  same  teacher,  variations  in  the  administration  of  the  tests, 
due  to  differences  between  teachers,  would  not  be  significant. 

At  the  close  of  each  semester  the  teachers  were  asked  to  report 
both  the  "final  grade"  and  the  "examination  grade"  for  each  stu- 
dent.2 In  most  cases,  the  "examination  grades"  were  reported  in 
terms  of  percents.  The  "final  grades"  were  generally  reported  in 
terms  of  letters,  as  follow: 

S=Superior 

E=Excellent 

G=Good 

F=Fair 

D=Failure 

For  the  purpose  of  combining  "grades,"  these  letters  were  as- 
sumed to  represent  the  following  numerical  ranges  on  a  scale  of  100 
percent: 

S  is  equivalent  to  95  and  over 

E  is  equivalent  to  85  to  94 

G  is  equivalent  to  75  to  84 

F  is  equivalent  to  65  to  74 

D  is  equivalent  to  55  to  643 

Plan  of  summarizing  data.  The  data  collected  were  sum- 
marized to  show  the  differences,  if  any,  which  existed  between  the 
final  achievements  of  pupils  in  the  large  classes  and  of  pupils  in  the 
small  classes.  Two  methods  of  summarizing  were  employed.  In 
the  first,  the  achievements  of  all  pupils  were  considered.  According 
to  the  second  method,  the  records  considered  were  limited  to  those 
of  pupils  in  the  large  classes  who  could  be  paired  with  pupils  having 
identical  scores  on  the  intelligence  test  in  the  corresponding  small 

The  following  tables,  in  which  the  data  for  high  school  classes  are  summarized, 
indicate  that  the  "examination  grades"  were  not  received  from  certain  classes. 

'The  midpoints  of  these  intervals  were  presumably  used  as  the  numerical  equiv- 
alents of  the  grades  expressed  in  terms  of  letter.  However,  Mr.  Stevenson's  report 
yields  no  information  on  this  point. 

26 


classes.  For  both  of  these  methods  two  tabulations  have  been  made. 
The  first  includes  all  classes,  and  the  second  only  those  pairs  of 
classes  in  which  the  large  class  was  at  least  twice  the  size  of  the  small 
class. 

Differences  in  achievements  when  all  pupils  are  consid- 
ered. Table  VI  illustrates  the  first  method  of  summarizing  the  data 
for  22  pairs  of  English  classes.  In  the  second  and  third  columns 
of  this  table  the  enrollment  in  the  large  classes  and  in  the  small 
classes  is  given.  The  quantities  recorded  in  the  three  columns  headed 
"Difference"  are  found  by  subtracting  the  quantities  in  the  two  col- 
umns immediately  preceding  the  difference  column.  The  number 
for  the  small  class  is,  in  every  case,  taken  from  that  for  the  large. 
Therefore,  a  positive  difference  means  that  the  large  class  is  superior 
in  the  trait  concerned,  and  a  negative  difference,  that  the  small  class 
is  superior.  The  line  at  the  bottom  of  the  table  gives  the  average 
for  each  column.  These  averages  may  be  taken  as  summarizing  the 
data  collected  from  these  22  pairs  of  English  classes,  although  the 
items  combined  are  not  entirely  comparable.  For  example,  different 
general  intelligence  tests  were  used  in  different  classes.  The  present 
writer  has  not  been  able  to  ascertain  the  particular  intelligence  test 
given  to  any  pair  of  these  22  pairs  of  classes.  It  is,  however,  difficult 
to  explain  the  extreme  differences  between  the  average  intelligence 
scores  of  classes  10  and  1 1  on  any  basis  other  than  the  use  of  different 
tests  in  these  two  pairs  of  classes.  Furthermore,  it  is  not  unlikely  that 
different  passing  marks  are  in  use  in  the  different  schools  in  which  the 
pairs  of  classes  were  taught.  If  this  is  the  case,  in  the  case  of  differ- 
ent pairs  of  classes,  both  the  average  term  grades  and  the  average 
examination  grades  are  on  different  scales. 

It  should  be  noted  that,  although  an  effort  was  made  to  organ- 
ize a  large  class  and  a  small  class  so  that  the  average  intelligence 
scores  would  be  approximately  the  same  for  the  two  classes,  this  was 
not  always  accomplished.  Because  of  conflicts  or  other  conditions 
that  could  not  be  disregarded,  it  was  not  always  possible  to  shift  pupils 
from  one  section  to  the  other  so  as  to  set  up  the  desired  class  organ- 
ization. 

Table  VII  summarizes  the  averages  for  the  classes  in  the  dif- 
ferent subjects.  In  interpreting  this  table,  it  is  necessary  to  bear  in 
mind  that,  with  the  exception  of  English  and  algebra,  the  number  of 


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pairs  of  classes  is  so  small  that  we  probably  should  not  consider  the 
result  representative.  Certainly,  little  if  any  significance  can  be  at- 
tached to  the  results  for  Latin,  history,  and  French.  The  average 
for  the  67  pairs  of  classes  is  the  weighted  average,  so  that  one  pair 
of  classes  does  not  influence  this  average  any  more  than  any  other 
pair. 

Table  VIII  presents  a  summary  for  those  pairs  of  classes  in 
which  the  large  class  is  at  least  twice  the  size  of  the  small  class.  By 
doing  this,  we  are  able  to  examine  the  achievements  of  pupils  in 
pairs  of  classes  where  the  difference  in  size  is  marked.  The  number 
of  classes  in  any  one  school  subject  is  so  small,  with  the  exception 
of  English,  that  we  are  probably  not  justified  in  drawing  any  conclu- 
sions for  the  separate  subjects. 

Differences  in  the  achievements  of  paired  pupils.  Table  IX 
is  similar  to  Table  VII,  the  only  difference  being  that  it  is  based 
upon  the  records  of  only  those  pupils  in  the  large  classes  who  could 
be  paired  with  pupils  in  the  corresponding  small  classes,  having  the 
same  scores  on  the  general  intelligence  test.  Since  the  pupils  were 
paired  on  the  basis  of  their  intelligence  scores,  the  average  general 
intelligence  of  those  taken  from  the  large  classes  would  be  identical 
with  the  average  general  intelligence  of  those  taken  from  the  corre- 
sponding small  classes.  Hence,  the  average  general  intelligence 
scores  are  omitted.  Table  X  is  similar  to  Table  VIII. 

Interpretation  of  the  tables.  When  all  67  pairs  of  classes 
are  considered,  the  average  of  the  general  intelligence  scores  for  the 
large  classes  is  almost  identical  with  that  for  the  small  classes,  the 
difference  being  only  one-tenth  of  a  unit.  This  unit  corresponds 
approximately  to  one  month  of  mental  age.  We  may,  therefore, 
consider  the  pupils  in  the  large  classes  equal  in  general  intelligence 
to  the  pupils  in  the  small  classes.  Both  the  average  "term  grade" 
and  the  average  "examination  grade"  are  slightly  larger  for  the  small 
classes. 

The  question  of  the  significance  of  the  difference  of  two  aver- 
ages is  involved  here.  Both  examination  grades  and  final  grades 
are  known  to  be  highly  subjective  and  to  involve  a  large  error  which 
is  a  combination  of  a  constant  error  and  a  variable  error.  Variable 
errors  tend  to  offset  each  other  in  an  average  because  some  of  them 
are  negative  and  some  positive.  On  the  other  hand,  constant  errors 


29 


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are  not  eliminated  in  averages.  The  number  of  pupils  included  in 
the  67  pairs  of  classes  is  sufficiently  large  so  that  the  average  grades 
include  a  variable  error  which  is  probably  so  small  as  to  be  negli- 
gible. For  example,  if  we  assume  that  the  probable  variable  error 
of  a  grade  is  as  much  as  10  points,  which  is  probably  in  excess  of 
the  actual  probable  variable  error,  the  probable  variable  error  of  the 
average  for  the  small  classes  would  be  less  than  three-tenths  of  one 
point.  In  the  case  of  the  large  class,  it  would  be  materially  less  than 
in  the  small  class.  The  constant  errors,  which  are  expressed  in  the 
tendency  of  some  teachers  to  give  higher  grades  than  others,  are 
probably  included  in  both  groups  in  approximately  the  same  pro- 
portion, since  the  same  teacher  assigned  grades  to  both  a  small  class 
and  a  large  class.  If  this  is  true,  a  difference  of  1.3  between  the 
average  term  grades  is  probably  significant,  although  there  is  a 
reasonable  doubt.  This  doubt  is  materially  increased  and  probably 
the  difference  loses  its  significance  when  we  recall  that  the  achieve- 
ments of  the  two  groups  of  students  were  not  measured  at  the  be- 
ginning of  the  experimental  period. 

When  we  consider  the  summaries  for  the  different  subjects,  we 
find  the  differences  between  the  average  achievements  of  the  pupils  in 
the  two  types  of  classes  materially  larger  in  a  number  of  cases  than 
the  differences  between  the  averages  for  the  67  pairs  of  classes.  How- 
ever, in  interpreting  these  differences  it  is  necessary  to  remember 
that  the  number  of  pupils  is  materially  less  and,  hence,  a  difference 
must  be  materially  greater  in  order  to  be  significant.  It  is  perhaps 
significant  that  negative  differences  predominate.  This  suggests  that 
the  average  achievements  in  the  small  classes  are  somewhat  superior 
to  those  in  the  large  classes,  but  in  drawing  conclusions  from  this 
condition  it  is  necessary  to  bear  in  mind  the  fact  that  the  achieve- 
ments of  the  students  were  not  measured  at  the  beginning  of  the 
experimental  period. 

When  we  turn  to  Table  VIII,  which  is  restricted  to  those  classes 
in  which  the  large  class  is  at  least  twice  the  size  of  the  small  class, 
we  find  that  the  pupils  in  the  small  classes  were  slightly  superior  in 
general  intelligence.  If  the  size  of  class  is  a  potent  factor  in  de- 
termining the  achievements  of  pupils,  we  should  naturally  expect  to 
find  a  greater  difference  in  the  achievements  of  the  two  types  of 
classes  than  we  found  in  Table  VIII.  The  fact  that  the  difference 

34 


is  less,  both  absolutely  and  relatively,  suggests  that  the  size  of  class 
is  not  a  potent  factor  in  determining  the  achievements  of  pupils. 
However,  the  number  of  pairs  on  which  Table  VIII  is  based  is  so 
small  that  no  great  importance  should  be  attached  to  this  observa- 
tion. 

When  we  examine  Table  IX,  we  find  that  the  differences  be- 
tween the  averages  for  the  67  pairs  of  classes  are  only  slightly  larger 
than  those  given  in  Table  VII.  In  general,  there  are  few  significant 
differences  to  be  noted  in  a  comparison  of  these  two  tables.  One  of 
the  most  significant  is  the  reversal  of  the  relative  achievements  of 
the  large  class  and  the  small  class  in  Latin.  In  Table  VII,  when  all 
pupils  were  considered,  those  taught  in  the  large  class  were  shown 
to  be  distinctly  superior  in  achievement.  When  only  the  paired 
pupils  were  considered,  those  taught  in  the  small  class  were  dis- 
tinctly superior  in  achievement.  Considering  the  table  as  a  whole, 
we  are  justified  in  asserting  that  it  tends  to  corroborate  the  interpre- 
tations suggested  for  Table  VII.4 

Conclusion:  relation  of  size  of  class  in  high  school  to 
school  efficiency.  The  tables  of  this  chapter  show  that  at  the  end 
of  the  experimental  period  the  achievements  of  the  students  in  the 
two  types  of  classes  were  approximately  equal,  and  there  is  a  slight 
indication  that  those  taught  in  small  classes  were  superior.  Since 
the  educational  investment  can  be  materially  decreased  by  increas- 
ing the  size  of  class  in  the  high  school,  one  might  infer  that  the  effi- 
ciency of  the  school  would  be  increased  by  organizing  classes  enroll- 
ing from  35  to  40  students  instead  of  classes  enrolling  from  20  to  25. 
In  addition  to  the  fact  that  there  are  several  uncontrolled  factors 
whose  influence  is  unknown,  it  is  necessary  to  bear  in  mind  the  exact 
conditions  of  the  experiment.  Since  the  same  teachers  taught  both 


4In  his  report,  Mr.  Stevenson  attempted  the  further  analysis  of  the  data  by 
ascertaining  the  percent  of  pairs  of  pupils  in  which  the  pupil  in  the  small  class  re- 
ceived a  higher  grade  than  the  corresponding  pupil  in  the  large  class.  When  all 
pairs  of  pupils  are  considered,  he  shows  that  only  in  40  percent  of  the  pairs  does 
the  pupil  in  the  small  class  surpass  his  mate  in  the  large  class.  However,  it  is 
impossible  to  draw  any  conclusion  from  this  fact,  because  we  do  not  know  the  per- 
cent of  pairs  in  which  the  two  pupils  received  the  same  mark.  Since,  in  a  majority 
of  the  cases,  the  grades  were  reported  in  terms  of  letters  and  only  five  marks  were 
recognized,  it  is  reasonable  to  expect  that  in  a  relatively  large  percent  of  the  cases 
bcth  of  the  paired  pupils  received  the  same  final  grade. 

35 


a  small  class  and  a  large  class,  there  was  no  difference  between  the 
total  amount  of  work  done  by  the  teachers  who  handled  the  large 
classes  and  the  teachers  who  handled  the  small  classes.  In  fact,  they 
were  the  same  teachers.  Thus,  this  experiment  failed  to  set  up  the 
conditions  of  large  classes  as  a  general  plan  of  organization  of  a  high 
school.  It  did,  however,  realize  the  conditions  which  not  infrequently 
exist  in  the  smaller  high  schools  where  it  is  desirable  to  have  a  few 
large  classes  assigned  to  teachers  who  are  given  compensating  small 
classes  or  who  have  the  number  of  classes  reduced  accordingly.  The 
results  of  the  experiment,  therefore,  can  be  applied  only  to  those 
situations  in  which  the  teaching  load  is  kept  constant.  In  such  cases 
the  evidence  collected  indicates  that  approximately  the  same  aver- 
age achievement  can  be  expected  from  the  pupils  taught  in  large 
classes  as  from  those  taught  in  small  classes.  In  other  words,  the 
results  of  this  experiment  indicate  that  there  is  no  loss  of  efficiency 
caused  by  organizing  a  few  large  classes  if  the  other  work  assigned 
to  the  teacher  is  such  that  the  teaching  load  is  not  increased. 

One  should  recognize  that  the  results  of  this  experiment  should 
not  be  applied  to  the  question  of  the  size  of  class  where  increasing 
the  size  of  class  results  in  a  distinct  increase  in  the  teaching  load. 
The  instruction  which  students  receive  is  given  partly  in  the  class 
room  and  partly  through  written  work  and  individual  conferences. 
In  such  subjects  as  English  composition,  algebra,  and  science  re- 
quiring laboratory  work,  it  is  customary  with  most  teachers  to  re- 
quire a  large  amount  of  written  work.  A  teacher  who  gives  instruc- 
tion to  five  classes  of  40  students  each  has  a  much  heavier  teaching 
load  than  the  teacher  who  instructs  five  classes  of  20  students  each, 
unless  he  introduces  compensating  changes  in  the  amount  of  written 
work,  in  the  method  of  handling  it,  and  in  the  number  of  individual 
conferences.  In  such  cases  the  question  of  class  size  is  so  intimately 
connected  with  the  method  of  instruction  that  we  are  not  justified 
in  drawing  any  inferences  from  an  investigation  in  which  the  method 
of  instruction  was  assumed  to  be  the  same  for  both  types  of  classes. 


36 


CHAPTER  V 
SUGGESTIONS  FOR  EDUCATIONAL  EXPERIMENTATION1 

The  two  studies  described  in  Chapters  III  and  IV  make  very 
slight  contributions  to  a  scientific  determination  of  the  relation  be- 
tween the  size  of  class  and  the  efficiency  of  a  school  system.  They 
do,  however,  seem  to  the  writer  of  this  chapter  suggestive  with  ref- 
erence to  the  procedure  of  educational  experimentation.  The  causes 
of  the  failure  of  these  studies  to  produce  reliable  and  significant  re- 
sults have  been  mentioned  in  the  two  preceding  chapters  but  they 
may  be  summarized  under  two  general  heads:  first,  failure  to  set 
up  and  maintain  appropriate  experimental  conditions  and,  second, 
the  lack  of  adequate  instruments  for  measuring  the  achievements  of 
pupils. 

A  prerequisite  for  setting  up  and  maintaining  appropriate  ex- 
perimental conditions  is  a  complete  analysis  of  the  problem  being 
studied.  The  various  factors  involved  must  be  recognized  by  the 
experimenter  and  the  possibility  of  any  relations  which  may  exist 
between  these  factors  must  also  be  considered.  For  example,  in  the 
high  school  many  factors  contribute  to  the  achievements  of  students, 
or  the  educational  output  of  the  school.  In  addition  to  the  size  of 
class,  which  is  the  factor  whose  relationship  to  school  efficiency  was 
studied,  it  is  necessary  to  recognize  methods  of  instruction,  the  per- 
sonality and  enthusiasm  of  the  teacher,  the  discipline  of  the  class 
and  of  the  school,  the  general  spirit  of  the  school,  the  general  atti- 
tude of  the  community  toward  the  school,  the  time  df  day  when  the 
class  recites,  the  textbooks  used,  the  equipment,  including  the  build- 
ing, the  "spiritual  composition"  of  the  class,  the  general  intelligence 
of  the  students,  their  nationality,  their  past  experience,  both  in  school 
and  out  of  school,  the  stage  of  advancement  reached  in  their  educa- 
tion, and  possibly  even  other  factors.  It  appears  likely  that  certain 
of  these  factors  are  interrelated.  The  size  of  class  is  likely  to  affect 
the  enthusiasm  of  the  teacher,  particularly  if  it  determines  the  in- 

lPrhis  chapter  has  no  counterpart  in  the  report  submitted  by  Mr.  Stevenson.  It 
is  entirely  the  contribution  of  the  present  director  of  the  Bureau  of  Educational 
Research. 

37 


structional  load  carried  by  the  teacher.  It  also  appears  that  some 
relationship  exists  between  the  size  of  class  and  methods  of  instruc- 
tion, and  between  the  size  of  class  and  discipline.  The  ex- 
istence of  a  functional  relationship  between  two  or  more  factors 
makes  it  impossible  under  normal  conditions  to  produce  variations 
in  one  factor  without,  at  the  same  time,  causing  changes  in  the  others. 
Failure  to  analyze  the  problem  sufficiently  will  frequently  cause  the 
results  of  an  educational  experimentation  to  have  little  significance, 
and  consequently  the  time  and  money  invested  in  the  study  will  be 
largely  wasted. 

When  one  considers  the  total  product  of  the  educational  pro- 
cess one  cannot  fail  to  become  impressed  with  the  inadequacy  of  our 
present  educational  tests  as  instruments  for  the  measurement  of  the 
various  elements  of  this  product.  In  the  study  relating  to  the  size 
of  class  in  the  elementary  school  a  more  elaborate  group  of  tests 
might  have  been  used,  but  even  if  this  had  been  done,  it  does  not 
appear  likely  that  one  would  be  justified  in  asserting  that  the  total 
product  of  education  had  been  measured.  In  the  high  school  no 
standardized  educational  tests  were  used.  It  was  attempted  to  have 
the  achievements  measured  by  means  of  a  final  examination  and  by 
the  term  "grade"  given  to  the  students.  The  writer  of  this  chapter 
is  not  aware  of  the  considerations  which  resulted  in  the  decision  not 
to  use  any  of  the  standardized  educational  tests  that  have  been  de- 
vised in  the  field  of  high  school  subjects,  but  it  is  likely  that  this  de- 
cision was  due  to  the  belief  that  none  of  the  available  educational 
tests  were  sufficiently  satisfactory  measuring  instruments  to  justify 
their  use  in  this  investigation.  The  present  writer  is  inclined  to  share 
this  belief.  Thus,  we  cannot  escape  the  conclusion  that  at  the  pres- 
ent time  we  do  not  have  available  instruments  for  measuring  the 
outcomes  of  teaching  which  permit  reliable  educational  experimenta- 
tion when  it  is  necessary  to  measure  the  total  product  of  instruction. 

Incidentally,  attention  may  be  called  to  the  fact  that  more  con- 
sideration should  be  given  to  the  errors  involved  in  the  data  and  to  the 
effect  of  these  errors  upon  the  results  of  statistical  calculations.  For 
example,  it  is  highly  important  to  know  what  significance  should  be 
attached  to  a  difference  between  two  averages. 

In  view  of  the  difficulties  encountered  in  setting  up  and  main- 
taining appropriate  experimental  conditions  and  in  view  of  the  im- 

38 


perfections  and  limitations  of  our  present  educational  tests,  it  is 
not  inappropriate  to  question  the  wisdom  of  undertaking  such  com- 
plex educational  experimentation  as  has  been  described  in  this  mon- 
ograph. It  is  true  that  there  are  many  educational  problems  which 
are  highly  important.  For  example,  an  increase  in  the  size  of  class 
would  result  in  a  material  reduction  in  the  educational  expenditures 
for  instruction.  A  reliable  scientific  determination  of  the  relation- 
ship existing  between  the  size  of  class  and  school  efficiency  would 
be  a  valuable  contribution,  but  it  is  doubtful  whether  such  a  deter- 
mination of  this  relation  is  at  the  present  time  possible. 

To  the  present  writer,  it  appears  highly  important  that  those 
engaged  in  educational  research  should  give  very  careful  considera- 
tion to  the  sort  of  problems  to  which  they  devote  their  energies. 
It  is,  of  course,  necessary  that  pioneer  work  be  done,  and  in  studies 
of  this  type,  it  is  not  always  possible  to  anticipate  the  limitations 
of  one's  procedure.  As  a  result  it  may  become  necessary  to  "scrap" 
a  project  because  of  the  defects  that  appear  in  the  course  of  one's 
work.  Such  losses  are  unavoidable  in  extending  the  frontiers  of  ed- 
ucational research.  When  an  investigation  is  not  pioneer  work  an 
experimenter  should  determine  the  limitations  of  his  procedure  in 
advance,  and  unless  it  appears  likely  that  information  of  considerable 
value  will  be  secured  in  spite  of  the  limitations  the  investigation 
should  not  be  undertaken.  The  fact  that  a  problem  is  important 
does  not  justify  its  study.  Educational  experimentation  which  in- 
volves the  use  of  faulty  method  and  faulty  instruments  not  only 
fails  to  make  adequate  contributions  to  our  educational  progress, 
but,  more  important,  it  tends  to  reflect  unfavorably  upon  the  ap- 
plication of  the  methods  of  research  to  the  field  of  education. 


39 


THE  UNIVERSITY  OF  ILLINOIS 

THE  STATE  UNIVERSITY 
URBANA 

DAVID  KINLEY,  PH.D.,  LL.D.,  President 


The  University  Includes  the  Following  Departments 

THE  GRADUATE  SCHOOL 

THE  COLLEGE  OF  LIBERAL  ARTS  AND  SCIENCES  (Ancient  and  Modern  Languages 
and  Literatures;  History,  Economics,  Political  Science,  Sociology,  Philosophy, 
Psychology,  Education;  Mathematics;  Astronomy;  Geology;  Physics;  Chemistry; 
Botany,  Zoology,  Entomology;  Physiology,  Art  and  Design) 

THE   COLLEGE   OF   COMMERCE   AND   BUSINESS   ADMINISTRATION    (General    Business, 

Banking,  Insurance,  Accountancy,  Railway  Administration,  Foreign  Commerce; 
Courses  for  Commercial  Teachers  and  Commercial  and  Civic  Secretaries) 

THE  COLLEGE  OF  ENGINEERING  (Architecture;  Architectural,  Ceramic,  Civil,  Elec- 
trical, Mechanical,  Mining,  Municipal  and  Sanitary,  Railway  Engineering,  and 
General  Engineering  Physics) 

THE  COLLEGE  OF  AGRICULTURE  (Agronomy;  Animal  Husbandry;  Dairy  Husbandry; 
Horticulture  and  Landscape  Gardening;  Agricultural  Extension;  Teachers' 
Course;  Home  Economics) 

THE  COLLEGE  OF  LAW  (Three-year  and  four-year  curriculums  based  on  two  years 
and  one  year  of  college  work  respectively) 

THE  COLLEGE  OF  EDUCATION 

THE  CURRICULUM  IN  JOURNALISM 

THE  CURRICULUMS  IN  CHEMISTRY  AND  CHEMICAL  ENGINEERING 

THE  SCHOOL  OF  RAILWAY  ENGINEERING  AND  ADMINISTRATION 

THE  SCHOOL  OF  Music   (four-year  curriculum) 

THE  LIBRARY  SCHOOL   (two-year  curriculum  for  college  graduates) 

THE  COLLEGE  OF  MEDICINE   (in  Chicago) 

THE  COLLEGE  OF  DENTISTRY  (in  Chicago) 

THE  SCHOOL  OF  PHARMACY  (in  Chicago;  Ph.G.  and  Ph.C.  curriculums) 

THE  SUMMER  SESSION  (eight  weeks) 

EXPERIMENT  STATIONS  AND  SCIENTIFIC  BUREAUS:  U.  S.  Agricultural  Experiment 
Station;  Engineering  and  Experiment  Station;  State  Laboratory  of  Natural 
History;  State  Entomologist's  Office;  Biological  Experiment  Station  on  Illinois 
River;  State  Water  Survey;  State  Geological  Survey;  U.  S.  Bureau  of  Mines 
Experiment  Station. 

The   library   collections   contain   May    1,  1922,  523,230  volumes  and  120,151   pam- 
phlets.    For  catalogs  and  information  address 

THE    REGISTRAR 

Urbana,  Illinois 


BULLETINS   OF    THE    BUREAU    OF    EDUCATIONAL    RE- 
SEARCH, COLLEGE  OF  EDUCATION,  UNIVERSITY 
OF  ILLINOIS,  URBANA,  ILLINOIS. 

Price. 

No.  I.     Buckingham,  B.  R.     Bureau  of  Educational  Research, 

Announcement,  1918-19 15 

No.  2.     First  Annual  Report 25 

No.  3.     Bamesberger,  Velda   C.     Standard  Requirements   for 

Memorizing  Literary  Material 50 

No.  4.     Holley,   Charles    E.     Mental   Tests    for    School   Use. 

(Out  of  print) 50 

No.  5.    Monroe,  Walter  S.    Report  of  Division  of  Educational 

Tests  for  1919-20 25 

No.  6,    Monroe,  Walter  S.    The  Illinois  Examination 50 


No.  7.  Monroe,  Walter  S.  Types  of  Learning  Required  of 
Pupils  in  the  Seventh  and  Eighth  Grades  and  in  the 
High  School 15 

No.  8.     Monroe,  Walter  S.    A  Critical  Study  of  Certain  Silent 

Reading  Tests 50 

No.  9.     Monroe,  Walter  S.    Written  Examinations  and  Their 

Improvement.     (In  preparation) 50 

No.  10.     Bureau  of  Educational  Research.     Relation  of  Size 

of  Class  to  School  Efficiency 50 


Syracuse,  n.  z. 

"AT.  JAM  21,  1908 


FOURTEEN  DAY  USE 

RETURN  TO  DESK  FROM  WHICH  BORROWED 


This  book  is  due  on  the  last  date  stamped  below,  or 

on  the  date  to  which  renewed. 
Renewed  books  are  subject  to  immediate  recall. 


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(B139s22)476                                         Umversuy^crf  California 

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